give me an example of Moment Magnitude Scale
The moment magnitude scale (Mw) is a measure of the size or magnitude of an earthquake. It is based on the seismic moment of the earthquake, which is calculated by multiplying the average slip on the fault by the area of the fault rupture and the rigidity of the rocks involved.
Here is an example of how the moment magnitude scale can be used to assess the magnitude of an earthquake:
Let's say a massive earthquake occurs along the San Andreas Fault in California. Scientists analyze the seismic data and calculate that the average slip on the fault was around 10 meters, the rupture area was 100 square kilometers, and the rocks had a rigidity of 30 gigapascals.
Using the formula for seismic moment (M0) = (average slip) x (rupture area) x (rigidity), we can calculate the seismic moment as follows:
M0 = 10 meters x 100 square kilometers x 30 gigapascals = 3 x 10^19 Nm.
Now, the moment magnitude (Mw) can be determined using the logarithmic relationship between Mw and seismic moment. The equation is:
Mw = (2/3) * log10(M0) - 6.0.
Plugging in our calculated seismic moment:
Mw = (2/3) * log10(3 x 10^19) - 6.0.
Mw = 7.8.
Therefore, the earthquake along the San Andreas Fault would be classified as a magnitude 7.8 earthquake on the moment magnitude scale (Mw).